Quite
a few people have been asking me questions about the number of points gained and
lost in the Ratings Central system. If you have read the scientific article in
the Journal of the Royal
Statistical Society you’ll appreciate that it’s not an easy question to
answer. In the email below I was able to give Richard a partial solution by
producing a table that shows the probability of a player winning based on the
difference in rating points between the two players. By way of example, if you
are rated 100 points higher than your opponent you will need to win 82% of your
matches against them to maintain that average difference of 100
points.

Breaking
news: I have managed to replicate the Ratings Central algorithm in a spreadsheet
and can now calculate the actual number of rating points that will be gained or
lost when you win or lose a match.

Note
that at this stage it has been written to only calculate point changes for one
match between two players. A tournament is more complicated because the initial
ratings of all your opponent’s are first adjusted for the results of all of the
other matches that they played in the tournament i.e. the results of all matches
need to be processed simultaneously. I’ll try to implement this in the future
but in the meantime the calculator in this attachment should closely replicate
the Ratings Central algorithm for point changes in a single
match.

To
use the spreadsheet you just need to enter values for both players into the
yellow cells on the “Calculator” tab. The resulting change in rating points are
shown in the blue cells in row 28.

I’ve
used the calculator to generate a few tables that demonstrate some of the main
features of the system. In this first table Player A defeats player B and gains
more rating points as the strength of his opponent increases. It also shows that
if your opponent is rated a long way below you there will be very little gain. Observe too that when both players have exactly the
same standard deviation that the points gained by the winner are the same as the
points lost by the loser.

Player
A

Player
B

A's

B's

Rating

SD

Rating

SD

change

change

1000

±
50

def

600

±
50

0

-0

1000

±
50

def

700

±
50

1

-1

1000

±
50

def

800

±
50

3

-3

1000

±
50

def

900

±
50

7

-7

1000

±
50

def

1000

±
50

15

-15

1000

±
50

def

1100

±
50

24

-24

1000

±
50

def

1200

±
50

32

-32

1000

±
50

def

1300

±
50

35

-35

1000

±
50

def

1400

±
50

37

-37

1000

±
50

def

1500

±
50

37

-37

The
standard deviation (SD) is a measure of the level of confidence in the rating
that has been assigned to a player by the algorithm. A high standard deviation
means that there is a greater possibility that your rating is not at the right
place. Generally, the more matches you play the more information the algorithm
has to determine your true playing strength with respect to other players and
your standard deviation will be low.

The
next table shows the importance of the standard deviation when calculating point
changes. In each match Player A defeats an opponent who has exactly the same
rating but I have used a variety of standard deviation values for Player B. The
table shows two things. Firstly, that you will gain more points for defeating a
player with a low standard deviation. This is because the algorithm assigns more
weighting to the result because it is more confident that your opponent really
is at the level indicated by their rating. Secondly, it shows the imbalance in
the points gained and lost by players with different standard deviations. The
player with the lowest standard deviation will always move a lot less than the
player with the higher standard deviation.

Player
A

Player
B

A's

B's

Rating

SD

Rating

SD

change

change

1000

±
50

def

1000

±
30

16

-6

1000

±
50

def

1000

±
40

16

-10

1000

±
50

def

1000

±
50

15

-15

1000

±
50

def

1000

±
60

15

-21

1000

±
50

def

1000

±
80

14

-35

1000

±
50

def

1000

±
100

13

-50

1000

±
50

def

1000

±
150

10

-91

1000

±
50

def

1000

±
200

8

-134

1000

±
50

def

1000

±
250

7

-177

The
above table also works in reverse. The player with the 250 standard deviation
would gain 177 points for defeating the player with the standard deviation of 50
but their opponent would only lose 7 points.

Take
a copy of the spreadsheet (see attachment below and have a play if you’re
interested.